Hi there,
So, you can "Hint" at a referral. What I mean is, you can say "Thanks so much for your time. You've definitely confirmed for me that this is a great place to work and I'll be planning to apply in the coming weeks. Are there any tips or pieces of advice you have for me?"
^This is the closest you can get to asking for a referral.
You also have a "Second chance", whereby you can send the Partner an email a few days before applying. Essentially let them know you are applying in the coming days, thank them again for the time.
In terms of how to conduct yourself during the call...
Ask For Yourself
While a coffee chat is a way for you to make a good impression, please remember that it's also about you making sure this job + path are right for you!
To prepare, think about things you'd like to learn about the company. Ask about your person's experience at the firm, where they've come from, if they have any advice for you etc. Be inquisitive and interested in what they have to say, and feel free to ask thoughtful follow-up questions.
Have Your Pitch Ready
In terms of what they'll ask you, make sure you have your 30 second pitch prepared! Who are you in a nutshell and why are you interested in BCG and strategy consulting?
Ask About Them
People love to talk about themselves. Just ask them what they've worked on recently or what their journey at BCG has been like. Importantly, do your research beforehand - find out what they've done and try and pick something from their past that looks interesting to you. Tailor your questions just like they tailor their FIT questions to your resume.
"So, how did you end up in the Industrial Goods sector?" "I saw you worked on a big digital transformation for a financial services company - I experienced one myself and it seemed so hard to move such a big organisation. What did you see as the major challenges and breakthrough moments?"
Ask insightful questions
Ideally, your questions should also show them that you're insightful, inquisitive, bright, thinking about current topics, etc. For example:
"I saw you worked on a big digital transformation for a financial services company - I experienced one myself and it seemed so hard to move such a big organisation. What did you see as the major challenges and breakthrough moments?"
"I know that x big trend is happening. I also know that y types of companies exhibit z traits. How do you reconcile this difference when ensuring y companies adopt x trends?
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